Problem: Simplify the following expression: $\dfrac{80t^3}{96t^3}$ You can assume $t \neq 0$.
Solution: $ \dfrac{80t^3}{96t^3} = \dfrac{80}{96} \cdot \dfrac{t^3}{t^3} $ To simplify $\frac{80}{96}$ , find the greatest common factor (GCD) of $80$ and $96$ $80 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5$ $96 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(80, 96) = 2 \cdot 2 \cdot 2 \cdot 2 = 16 $ $ \dfrac{80}{96} \cdot \dfrac{t^3}{t^3} = \dfrac{16 \cdot 5}{16 \cdot 6} \cdot \dfrac{t^3}{t^3} $ $\phantom{ \dfrac{80}{96} \cdot \dfrac{3}{3}} = \dfrac{5}{6} \cdot \dfrac{t^3}{t^3} $ $ \dfrac{t^3}{t^3} = \dfrac{t \cdot t \cdot t}{t \cdot t \cdot t} = 1 $ $ \dfrac{5}{6} \cdot 1 = \dfrac{5}{6} $